With the development of the technologies of the Internet of Things and the
logistical network, the information about more categories can be achieved and
comprehensively utilized in an integrated information system (Ning
and Wang, 2011; Mulligan, 2010). Supported by the
superior available of the logistical network, the applications to the logistical
services based on the technologies become one of the hot research spots (Grandinetti
et al., 2012; Creazza et al., 2012).
Based on the integrated logistical information (Amaya et
al., 2010) describe a solution procedure for a capacitated arc routing
problem with refill points and multiple loads. By presenting an integer formulation
and a route first-cluster second heuristic procedure, the proposed model can
simultaneously determine the vehicle routes that minimize the total cost of
the two vehicles.
Utilizing the static and dynamic information of the logistical network, Perugia
et al. (2011) put forward a solution to the home-to-work bus service
in urban zone. In the solution, a model with a cluster routing algorithm is
designed to scheme the routing and the bus stop location based on the real-time
information achieved from the metropolitan transportation networks. By the search
algorithm, the restrictions about efficiency, equity and effectiveness come
to an equilibrium state.
In contrast to search feasible scheme utilizing the integrated logistical information,
the exploring of the optimization solution is another key application in the
research of the logistical service (Leiva et al.,
2010; Iyoob and Kutanoglu, 2013). To the logistical
service with multiple categories of elements involved, the design of the optimization
algorithm is usually very complicated work due to the complexity of the logistical
information (Miranda and Garrido, 2009; Pishvaee
et al., 2010). In consideration of constrains relative to riding
in the urban routing networks, a framework is put forward to achieve a set of
Pareto-optimal feasible solution by Chang and Yen (2012).
Utilizing the information about the urban routing network, the city-courier
routing and scheduling problem is transferred into a multiple routing salesman
problem with multiple objectives. In order to decrease the expenditures relative
to school operations and student transportation, Mandujano
et al. (2012) proposed an optimization scheme, in which a methodology
with two mixed-integer programming models is used to reduce transportation costs
by optimize the transportation of students and the location of the schools for
the designated area. In order to meet the coordination requirements of a supply
chain, Yildiz et al. (2010) proposed a modified
mixed-integer programming methodology, by which the probability to reduce the
cost of distribution is enhanced.
By comprehensively analyzing the algorithm mentioned above, it is the common
insufficiency that the time cost of the optimization procedure increases rapidly
and unevenly with the dimension increasing of the logistical network. To solve
the problem, an optimization model based on Hamming competitive neural network
is put forward. In the proposed model, the goods dispatching requirement of
the logistical service is formulated by the combination of preconditions. Then
a input vector is reformulated by the combination of preconditions and taken
as the input data to the modified particle swarm optimization algorithm with
the Hamming competitive neural network algorithm involved. Simulative experiments
indicate the proposed model is efficient and effective to the optimization of
the logistical service.
DESCRIPTION TO THE STATIC AND DYNAMIC INFORMATION ABOUT THE LOGISTICAL NETWORK
To implement the logistical services, the goods ready to be delivered distributed
in the service spots should be loaded and dispatched by proper transport utility
and route selection. The service spots and the routes connected with the service
spots consist of the backbone of the logistical network (Song
and Dong, 2012). The set S = (s1, s2, ..., sn)
represents the set of the service spots. Figure 1 represents
a logistical network with eight service spots and ten routes. In the figure,
denotes a service spots in the backbone of the logistical network and ↔
expresses the route between two service spots. When a pack of goods is required
to be dispatched from a service spot to another, a proper routes combination
through which the pack of goods can be transported to the destination can be
selected by certain approaches. For example, the routes combination for the
pack of goods which should be dispatched from the service spot S3
to the service spot S6 can be S3→S1→S6,
S3→S9→S6, or S3→S5→S4→S8→S6
according to the selection strategies.
Correspondingly, the dynamic information of the logistical network consists
of not only the back bone but also the goods distribution at the service spots
and the real-time information of the transport utilities with goods at the designated
time. In Fig. 2, the dynamic information of a certain time
point is shown as an example of the running logistical network. In the figure,
describe a pack of goods waiting at a service spot S1 and to be dispatched
to the destination S4. Accordingly, the denotation ,
which is at the route between the service spot S1 and S2,
represents a transport utility with or without goods moving from the service
spot S1 and S2 by the route between them.
||Logistical network with eight service spots and ten routes
||Dynamic state of the logistical network at certain time point
CRUCIAL FACTORS ABOUT THE LOGISTICAL SERVICE OPTIMIZATION
The service spots take charge of the receiving and dispatching of the goods in the logistical network. In the two figures above, the basic information about the logistical service scheme designing is represented in detail.
In order to comfort to the requirement of the algorithm and service scheme designing, the packs of goods are expressed specially. In the proposed model, a pack of goods being dispatched from one service spot to another is expressed by three parameters. The first and second parameters are the service spot of departure and the service spot of destination, respectively. The Carrying Capacity Requirement (CCR) of the packs of goods is taken as the third parameter.
The CCR can be the unit of weight or bulk. For sake of expressing comprehensively, The CCR is put forward to describe the carrying capacity requirement of goods uniformly. As an integrated logistical network, the relationship among the service spots and the packs of goods being dispatched can be represented by a matrix as follows:
In the matrix, lij denotes the CCR of goods which will be transfer
from the service spot si to the service spot sj. The matrix
which is named as [Mij]nxn can integrated express the
requirement of the goods being dispatched. For a designated period of time,
the goods in the logistical network is determined and can be described by a
set G = (g1, g2, ..., gs). Let
denote the subset of G which consists of packs of goods with the service spot
of departure Si and the service spot of destination Sj
and ccr (gi) is the CCR of the gi, then lij
can be represented as:
In order to implement the task of the goods dispatching, the states about the
transport utilities are also key parameters. As the carrying capacity of all
the transport utilities usable is constant, the location distribution and the
goods on loading of the transport utilities will influence the designing of
the proper scheme for the goods dispatching. Let the set T = (t1,
t2, ..., tm) represent the available transport utility
set of the logistical network. For the sake of meeting the information requirement
of the transport utilities for the logistical service scheme designing, the
vectors Vt and Vc are put forward to represent the location
distribution and the goods on loading of the transport utilities:
In the vector Vt, the element si means the transport
utility with the order number i is going to or at the service spot with the
order number si. To meet the need of convenient denotation, si
represents a order number of a service spot and i is the order number of the
transport utility. If si is the order number the service spot sj,
then the value of the si is j. In the vector Vc, the element
li means the CCR of the goods on loading of the transport utility
with the order number i. To comprehensively represent the carrying capacity
distribution of the logistical network, the information of the vectors Vt
and Vc can be fused into the following vector:
In the vector Vf, the element fi represents the carrying capacity available at the service spot si during the designated time period, which is the comprehensive information of the transport utilities going to or at si and the CCR of goods on loading of the transport utilities.
Summarily, the matrix [Mij]nxn and the vector Vf are preconditions to the drawing up of the logistical service scheme. Consequently, the matrix and the vector can be taken as the crucial information to the logistical service optimization.
OPTIMIZATION MODEL TO THE LOGISTICAL SERVICE
Algorithm for the optimization of the logistical services: At a designated time point, given the real-time information of the logistical network, there are usually a great many feasible service schemes to accomplish the task of all goods dispatching. The optimization of the logistical service is the procedure of searching for the proper service scheme with cost expenditure as small as possible. The cost expenditure mainly depends on the moving distance and the per unit distance cost expenditure of every transport utility. To the service scheme designing, accomplishing all tasks of goods dispatching is a basic constraint. For the sake of representing the basic constraint, the following sequences are put forward to denote the CCR of the goods loading on and unloading from the transport utility ti with time going on:
With the logistical network running on ceaselessly, the transport utility ti
loads and unloads the packs of goods and the sequences above are achieved in
order. To conveniently describe the service scheme, every two elements of the
two sequences with identical order number make up a pair. For example,
is pair to represent the CCR of goods loading on and unloading from the transport
utility ti at a certain service spot. For meaningfulness, the two
elements of a pair should not be zero simultaneously. That one element of a
pair is zero means either loading or unloading is taken place.
Based on the denotation above, the goods dispatching constraint can be represented as follows:
Let P denote the set of pairs which the transport utilities will generate in the designing service scheme. In the above equation, Sx (p) is the subset of P which consists of the pairs generated at the service spot Sx. The denotation relayx expresses the CCR of goods will be relayed by the service spot Sx. In other words, relayx, the CCR of goods relayed from Sx is unloaded by some transport utilities and loaded by others to relay on. The relay of the goods plays a role in better utilization of the carrying capacity of the transport utilities. In order to simplify the description of the constraint, let Eq. 2 be subtracted by Eq. 3 and then:
The carrying capacity of every transport utility is another constraint when the packs of goods are unloaded and loaded at every service spot. The constraint can be represented as follows:
is a pair in the service scheme designing.
In the designed service scheme, every packet of goods is transferred by the
relay of the transport utilities and moves from one service spot to another
by in order. Consequently, the transport utility a pack of goods being loaded
on and the packs of goods a transport utility loading on is probable to change.
G (ti, sj) represents the set of the packs of goods being
loaded on ti when ti leaves from sj to another
service spots and then the variation of the set of the packs of goods being
loaded on ti in a designed service scheme can be expressed by a sequence
Accordingly, in the designed service scheme, a pack of goods ga
with the service spot of departure sp and the service spot of sq
destination should be appeared in such a sequence as:
G (ti1, sj1), G (ti2,
sj2), ......, G (tic, sjd), 1≤ix≤m,
Let Dis (si, sj) represent the distance between the service spots si and sj and then the cost expenditure only considering the sum distance of all transport utilities can be expressed as:
In the equation above, G (ti, sjx)∈Seq (ti) is the sequence of the sets of the packs of goods ti being loaded on during the designed service scheme without the last element of the sequence.
From the representation of the constraints and the equation of the cost expenditure,
the designing of the service scheme is related to complicated arithmetic and
set operations. To accomplish the optimization by the proper service scheme
selection, the Particle Swarm Optimization (PSO) algorithm is chosen. In the
PSO algorithm, the selected service scheme is represented as the solution vector
space (Selleri et al., 2006). By the overlapping
generations from one feasible service scheme to other, the optimized scheme
will be achieved. The following are equations for overlapping generations of
a particle in the PSO algorithm:
In the equations, p [i] represents a particle.
(t) is the feasible service scheme of current iteration. The denotation
(t+1) is the feasible service scheme of the next iteration.
(t+1) are the variation of the feasible service scheme of the last and the current
overlapping generation. c1 and c2 are constant quantity
and taken as the learning coefficients. r1 and r2 are
random values in value zone (0, 1). In PSO algorithm, a group of particles are
selected to walk in the feasible solutions. pbestp[i] (t) is the
extremum point of the particle p[i] until the current iteration. Correspondingly,
gbest(t) is the extemum point of the particle group until the current iteration.
From the description above, the iterations of the particles is random walking
in feasible zone of the solution under the control of the pbest of the particle
and the gbest of the particle group (Prado et al.,
2010). As the calculation of cost expenditure and the constraints is related
to the set operation in the service scheme of this study, the iteration formulas
above are modified and the following iteration equations are created (Thakker
et al., 2009):
In the above equations,
(t) is a feasible service scheme vector space. φ (,
is a function to achieve a service scheme (maybe infeasible) which is approximate
to both and
by the random modification of .
The function ξ (,
is used to achieve a feasible service scheme in midway of transforming
Optimization strategy based on the hamming neural network: The much more computation complexity of the cost expenditure, the constraints and the PSO algorithm with respect to the large scale of the logistical network makes the optimization of logistical service being a time consuming procedure. To enhance the real-time performance, another optimization strategy should be utilized.
With respect to the optimization procedure, the beginning of it is achieving feasible service scheme based on a matrix [Mij]nxn and a vector Vf and considering the constraints. In other words, an optimization feasible service scheme is corresponding to a combination of a matrix [Mij]nxn and a vector Vf as the preconditions. Usually, that the preconditions are similar means the optimization feasible service schemes are also approximate. Consequently, a designated logistical network will achieve a certain number of combinations of the preconditions at first. And meanwhile, the corresponding optimization feasible service schemes are also acquired. Then the later optimization procedure can be simplified to finding a combination of the precondition having been appeared formerly. Finally, the modified PSO can be started with the optimization feasible service scheme corresponding to the found combination. Owing to the similarity of the two combinations of preconditions, their optimization feasible service schemes are also approximate. As a result, the later optimization procedure is started directly at the point near to the optimization point with the modified PSO algorithm and the computation efficiency will be much enhanced.
In order to conform to the requirement of the similar combination selection,
the Hamming neural network with competitive learning feature is employed. The
Fig. 3 represents the construction of the Hamming competitive
neural network. In order to improve the computation efficiency of the optimization
procedure of logistical service described above, the two layers competitive
neural network is put to use (Ghanavti and Shomalnasab,
2009). In the competitive network, the input is a vector. Consequently,
the combination of the preconditions is reformulated to the following vector:
The vector above consists of the elements of the horizontal vectors of matrix [Mij]nxn connected by order and the vector Vf being appended.
In the first layer of the competitive Hamming neural network, a combination
of preconditions reformulated to a R dimensions vector (R = nx(n+1)) is taken
as the input waiting for finding the most similar vector to achieve the optimization
service scheme by further computation. The denotation W1 is the weight
matrix consisting of selected S number of R dimensions vectors which are corresponding
to the combinations of preconditions having achieved the optimization service
schemes. A selected R dimensions vector transposed becomes a horizontal vector
of W1 which becomes the prototype patterns (Guimaraes
et al., 2006). The denotation b1 is the bias vector which
is set equal to the number of the elements of the input vector. Consequently,
W1 and b1 can be represented as:
Summarily, the output of the first layer a1 can be expressed as the follows equation:
The outputs of the first layer indicate the correlation between the prototype patterns and the input vector. In contrast, the second layer is the competitive layer in which the neurons are initialized with the outputs of the first layer. Then the neurons compete with each other to determine a winner. After the competition, only one neuron will have a nonzero output. The winning neuron indicates which prototype is the most correlative to the input vector and the winner is selected to be used to further optimize the logistical service.
The first layer output a1 is used to initialize the second layer, that is to say:
Then the output of the second layer is updated according to the following recurrence relation:
The weight matrix W2 of the second layer is set so that the diagonal elements are 1 and the off diagonal elements have a small negative value. Then the elements of W2 can be represented:
As a result, at each iteration, the output of each neuron will decrease in proportion to the sum of the output of the other neurons. The output of the neuron with largest initial condition will decrease more slowly than that of the other and eventually the neuron will be the only one with positive output and becomes the winner.
Utilizing the competitive Hamming network, the procedure of the optimization
will be reorganized. When initializing, a table named Prototype Selection Table
(PST) is created to record the input vector and the corresponding optimization
service scheme. Meanwhile, a positive integer number S should be given as the
row vector number of W1, namely, the number of the prototypes. At
the beginning, the row vector number of W1 named as
is set to 0. When the first logistical service is submitted and the combination
of preconditions is reformatted to the format of the input vector and executes
the optimization procedure without the Hamming neural network involved because
of no prototype available. After the optimization service scheme having been
achieved, the input vector accompanying with the optimization service scheme
and a positive integer number μ will be acquired. The triple be inserted
into the PST as a record for further use. At this time, there are only one vector
can be selected as a prototype in which the value of
is set to 1. When 0<<S,
the optimization of the logistical service is executed with the Hamming neural
network involved. After the optimization finished, the input vector is selected
as a prototype and
and correspondingly, the information will be inserted into the PST. When the
Hamming neural network is involved in the optimization, a prototype becomes
the winner a time. Then the value μ recorded in PST according to the winner
is added by 1. On the contrary, the failure is subtracted by 1. Until
= S , the number the selected prototype will not increase. If the value μ
recorded in PST according to a prototype is decreased to negative number, the
prototype is a new prototype which is last input vector.
Simulative experiments and experimental analysis: As the complexity
of the components and their interaction in the logistical network, the effectiveness
and the efficiency of a logistical service model are usually testified by the
simulative experiments (Yaghini et al., 2012;
Thompson and Hagstrom, 2008). In the simulative experiments,
the logistical networks with different dimensions are simulated. The Table
1 lists the dimensions of the logistical networks in the simulative experiments.
To represents the dimensions of the logistical networks, two factors are selected.
The first one is the Number of the Service Spots (NSS), which the dimension
of the key elements in the logistical network. The second one is the average
number of the packs of goods (ANPD) dispatched during a certain period of time,
which the service dimension of the logistical network (Castillo-Villar
et al., 2012; Abu-Ali and Hassanein, 2008).
Five simulative experiments are implemented with the dimension listed in Table
1. In each experiment, the optimization procedures with and without Hamming
competitive network (denoted by With HCN and Without HCN, respectively) are
||Configurations of the logistical network in the simulative
||Average time cost according to the optimization procedures
with and without HCN
|| Comparison of ACEMR and CEOSS
For every procedure, about 200 input vectors reformatted by the combinations
of preconditions are input to achieve the optimization service schemes. The
average time cost for achieving an optimization service scheme is represented
in Fig. 4. Figure 4 indicates that the time
cost of HCN is much smaller with the dimension increasing of the logistical
network. Consequently, utilizing the Hamming competitive network, the optimization
efficiency will be enhanced especially when the dimension of the logistical
network is large enough.
In the procedure of the optimization for a combination of the preconditions
without the Hamming competitive network involved, a series of feasible service
schemes are presented and the cost expenditure is achieved as midway results.
The comparison between the Average Cost Expenditure of the Midway Results (ACEMR)
and the cost Expenditure of the Optimized Service Scheme (CEOSS) indicates the
optimization efficiency of the proposed algorithm (Becker
et al., 2012; Biehl et al., 2007).
Figure 5 represents the comparison of ACEMR and CEOSS with
the variation of ANPD and the fixed number of service spots (NSS = 51). The
variations of ACEMR and CEOSS demonstrate that the CEOSS is much less and increases
more slowly than ACEMR, which indicates the proposed algorithm is effective
in the optimization and the optimization effectiveness is more remarkable accompanying
with the dimension increasing of the logistical network.
Summarily, the optimization model of the logistical service can not only enhance the efficiency in reducing the time cost of the optimization procedure but also is more effective to achieve the optimized service scheme.
To solve the problem that the time cost of the optimization procedure rapidly and unevenly increases with the dimension increasing of the logistical network, an optimization model of logistical service is put forward. In the proposed model, the goods dispatching requirement and the other static and dynamic information of the logistical network are taken as the combination of preconditions and the constitution of the feasible service scheme. By formulate the combination of preconditions into the input vector with designated format, the input vectors are corresponding with the optimized service scheme. Taken the historical input vectors as prototypes, the Hamming competitive neural network algorithm can enhance the efficiency and effectiveness of the optimization procedure.
This work was funded by the Science and Technology Department of Tangshan City (No.12140201A-7).